On Solving the Minimum Spanning Tree Problem with Conflicting Edge Pairs

Abstract

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In recent years, several heuristic and exact approaches have been proposed to tackle this problem. In this paper, we present a mixed-integer linear program not previously applied to this problem, and we solve it with an open-source solver. Computational results for the benchmark instances commonly adopted in the literature of the problem are reported. The results indicate that the approach we propose obtains results aligned with those of the much more sophisticated approaches available, notwithstanding it being much simpler to implement. During the experimental campaign, six instances were closed for the first time, with nine improved best-known lower bounds and sixteen improved best-known upper bounds over a total of two hundred thirty instances considered.